Artículo

A Singular Semilinear Elliptic Equation with a Variable Exponent

Journal ar
Advanced Nonlinear Studies
  • Volumen: 16
  • Número: 3
  • Fecha: 01 agosto 2016
  • Páginas: 491-498
  • ISSN: 15361365
  • Tipo de fuente: Revista
  • DOI: 10.1515/ans-2015-5039
  • Tipo de documento: Artículo
  • Editorial: Walter de Gruyter GmbH info@degruyter.com
© 2016 by De Gruyter. In this paper we consider singular semilinear elliptic equations with a variable exponent whose model problem is-¿ u = f (x) u ¿ (x)in ¿, u = 0 on ¿. Here ¿ is an open bounded set of R N, ¿ (x) is a positive continuous function and f (x) s a positive function that belongs to a certain Lebesgue space. We prove that there exists a solution to this problem in the natural energy space H 0 1 (¿) when ¿ (x) ¿ 1 in a strip around the boundary. For another case, we prove that the solution belongs to H loc 1 (¿) and that it is zero on the boundary in a suitable sense.

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